Recursive analytical formula for the Green's function of a Hamiltonian having a sum of one-dimensional arbitrary delta-function potentials

The Green's functions of one-dimensional Hamiltonians containing, respectively, one and two delta-function potentials are derived by analytically summing over the corresponding Lippmann-Schwinger series. A generalization of this procedure leads to an explicit recursive formula for the Green's function G⁽ⁿ⁺¹⁾ corresponding to a Hamiltonian containing a sum of n+1 delta-function potentials of arbitrary positions and strengths in terms of G⁽ⁿ⁾ and the additional n+1 delta-function potential parameters.